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3x3

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的一
2 2 2

x2
X-X ×
2n

2aa2 2.403
m-2n
1-4 22 3 3x3
X

ED,
3n

6 2.403 a 2.4.605 -3n - 6

X

3.5x4
-DQ
X

Х 4n

8 2.4.6a5 a2 2.4.6.8a? in - 4n 1 8 3,5x4

2

3.5.735 EQ= Х

x 5n

10 2.4.6.8a7 aa 2.4.6.8.10a. &c.

&c.

&c.
Therefore (a2-+x)=
x2

3.5x4 3.5.725
at
+

-&c. 2a 2.4a3 2.4.6a5 2.4.6.8a7 2.4.6.8.10a9 Where the law of formation of the several terms of the series is sufficiently evident.

1 2. It is required to convert or its equal (at

(a + b)2 b)-, into an infinite series.

b
and 2, or m=-2 and n=1;

n whence

3x3

+

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т

Here p=a,

a

.

.

the first of these expressions may be exhibited in the more simple form

m(m 1 mm-1) (a+x)=am tu mamic+ amo? +

1

1 2 (m-2)

am-32%.

3 m(m— 1) (m-2) [m-(n-1))a"acmate

1... 3, 4 Where the last térm is called the general term of the series, beCaus. if 1 2, 3, 4, &c. be substituted successively for n, it will give

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ali the rest.

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CQ=

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3::2
X Х

2.495

3 5x3 2.4.6a?

3n

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4. It is required to convert V9, or its equal (8+1)*

into an infinite series.

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Therefore 9= 1 1

5

5.8 2+

3.22 3.6.24' 3.6.9.27 3.6.9 12.210

3.6.20+

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5.8.11 3.6.9. 12.15.213

&€.

5. It is required to convert ✓2, or its equal (1+1), into an infinite series.

1 1 3 3.5 3.5.7 Ans. 1+

-&c. 2 2.4.2.4.6 2.4.6.8 2.4.6.8.10

+

+

6. It is required to convert v7, or its equal (8-1)},

into an infinite series.

1

1 Aps. 2

3.22 3.6.24

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7. It is required to convert V240, or its equal (243 - 3), into an infinite series. 1

4.9

4.9.14 Aps. 3

5.33 5.10.37 5.10.15.31 5.10.15.20.315

series.

8. It is required to convert (a+r)# into an infinite Ans. a}{1+

&c.}

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3x3 2.4.6a3

3.5x4 2.4.6.8a4

2a 2.402

3. It is required to convert (a+b)} into an infinite

series.

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series.

10. It is required to convert (a-b) into an infinite ał{1

&c.}

Ans.

6

362 4a 4.8a%

3.763 4.8.12a3

3.7.1164 4.8.12.1604

11. "It is required to convert (a+x)$ into an infinite series.

23
X2

4.723 4.7.1035 Ans.a {1+

ta
3a 9a2 92 a 3 92 12a" 92.12.15a5

4x3

+

&c.}

12. It is required to convert (1-2)} into an infinite series.

2x 2.3x3 2.3.8x3 2.3.8.13.04 Ans. 1

&c. 5 5.10 5.10.15 5.10.15.20

1

>

1 13. It is required to convert

or its equal

(a£x)? (a+-x):2 into an infinite series. 1

3x2 3.5x 3 3.5.7x4 Ans. 1# +

# &c.} 2a ' 2.402 2.4.6a3' 2.4.6.804

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+

(a+x)#

14. It is required to convert

or its equal (a+x)} into an infinite series.

2x2

2.5x3 2.5.8.04 Ang. a}{

1+

3a +3.6.az F3.6.9a37 3.6.9.12a4

F &c.}

1 15. It is required to convert -, or its equal

(1+x)} (1+x)} into an infinite series.

6x? 6.9x3 6.9.14x4
Ans. 1.

to
5.10 5.10.15' 5.10.15.20

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16. It is required to convert

or its equal (a +x) (a2--x2)), into an infinite series.

X2 23

3x4 3x5 5.36 5x7
Ans. -+
.

+

ta +

203894 292

-&c.

+
8a5 ' 16x6..' 1697

ts

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